Esther drove to work in the morning at an average speed of 45 mph and returned home in the evening at an average speed of 30 mph. If she spent a total of one hour commuting to and from work, how many miles did she drive in the morning?
The answer is 18 mi. Can anyone explain why?
2007-01-20 12:21:54 · 7 answers · asked by EF 2 in Science & Mathematics ➔ Mathematics
Let t1 be the time driving to work. Then 1-t1 is the time returning home.
Balance by the same distance:
45t1 = 30(1-t1)
Solve for t1,
t1 = 30/75 = 0.4 hrs
The distance she drove in the morning
= 45t1
= 18 miles
2007-01-20 12:29:45 · answer #1 · answered by sahsjing 7 · 0⤊ 0⤋
Let t be the time spent driving in the morning. Then her total distance driven to work was 45t. The total time spent back and forth is one hour, so the time spent coming back was 1 - t. This means the distance she traveled on her way home was 30(1-t).
It's probably safe to assume that she drives the same route to work and from work, so the distance of her trip to work is equal to the difference she drives home every night. This means 45t = 30(1-t).
Solve this for t to get the total time she spends in the morning. To get the distance, just multply your answer by 45 before 45t is supposed to give us the distance. You'll wind up with 18 miles.
2007-01-20 12:29:56 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Let x be the distance
v=x/t so t = x/v
then x/45 + x/30 = 1
then solve for x
18/45+18/30 = 2/5+3/5 = 1 right
2007-01-20 12:30:00 · answer #3 · answered by Theta40 7 · 0⤊ 0⤋
The distance from home to work and from work to home is equal.
If t is the amount of time it takes her to get to work (in hours), then 1 - t is the amount of time it takes her to get home:
rate × time = rate × time
45t = 30(1 - t)
45t = 30 - 30t
75t = 30
t = 0.4
So it took her 4/10 of an hour to get to work, at 45mph:
4/10 hour(45 miles/hour) = 18 miles.
2007-01-20 12:29:13 · answer #4 · answered by Jim Burnell 6 · 0⤊ 0⤋
Assume distance b/t home and work is 'x'
Recalling that: Distance = Velocity * time; time=Distance/Velocity
Time to work: x/45
Time to home: x/30
Total time = 1 hour = x/45 + x/30 = (2x + 3x)/90 = 5x/90 ==> x=90/5=18
2007-01-20 12:27:34 · answer #5 · answered by mjatthebeeb 3 · 0⤊ 0⤋
This is a [time] = [distance] / [rate] problem.
Let
d = distance one way
Time = 1 = d/45 + d/30
90 = 2d + 3d = 5d
90/5 = d
18 = d
The distance she drove in the morning is d = 18 miles.
2007-01-20 12:48:54 · answer #6 · answered by Northstar 7 · 0⤊ 0⤋
use d=rt
you know rate
and total time = 1
d/r=t
let x be the distance
x/45 is time to work
x/30 is time home
time to work +time home =1hour so
x/45+x/30=1
get lcd
2x/90+3x/90=1
5x/90=1
so
5x=90
x=18
2007-01-20 12:35:38 · answer #7 · answered by dla68 4 · 0⤊ 0⤋